Outer bounds employ the extremal entropy inequality as well as a bounding of the performance of a discrete, memoryless, multiuser, multilevel broadcast channel. For several cases, inner and outer bounds are established that either partially meet, or the gap diminishes with increasing coherence times.We propose a Hamiltonian-based approach to the nonextensive thermodynamics of small systems, where small is a relative term comparing the size of the system to the size of the effective interaction region around it. https://www.selleckchem.com/products/s64315-mik665.html We show that the effective Hamiltonian approach gives easy accessibility to the thermodynamic properties of systems strongly coupled to their surroundings. The theory does not rely on the classical concept of dividing surface to characterize the system's interaction with the environment. Instead, it defines an effective interaction region over which a system exchanges extensive quantities with its surroundings, easily producing laws recently shown to be valid at the nanoscale.We consider a nonparametric Generative Tree Model and discuss a problem of selecting active predictors for the response in such scenario. We investigated two popular information-based selection criteria Conditional Infomax Feature Extraction (CIFE) and Joint Mutual information (JMI), which are both derived as approximations of Conditional Mutual Information (CMI) criterion. We show that both criteria CIFE and JMI may exhibit different behavior from CMI, resulting in different orders in which predictors are chosen in variable selection process. Explicit formulae for CMI and its two approximations in the generative tree model are obtained. As a byproduct, we establish expressions for an entropy of a multivariate gaussian mixture and its mutual information with mixing distribution.Carbon emission control is an urgent environmental issue that governments are paying increasing attention to. Improving carbon market transaction efficiency in the context of China's power industry is important for green growth, low carbon transmission, and the realization of sustainable development goals. We used the entropy-weighted Technique for Order Preference by Similarity to an Ideal Solution (TOPSIS) method in this empirical study to analyze the carbon market transaction efficiency of China's power industry. The results showed that the Beijing carbon market has the highest transaction efficiency, followed by those of Guangdong Province and Shenzhen City. Hubei Province also has a relatively high carbon market transaction volume and turnover; its transaction efficiency ranks fourth. Shanghai, Tianjin, and Chongqing are the lowest-ranked regions, having carbon markets with relatively low trading volume and turnover. We, therefore, recommend that to develop a unified national carbon market, governmental agencies at all levels should equitably allocate carbon; strict regulations and penalties are also needed.We introduce a family of models, which we name matrix models associated with children's drawings-the so-called dessin d'enfant. Dessins d'enfant are graphs of a special kind drawn on a closed connected orientable surface (in the sky). The vertices of such a graph are small disks that we call stars. We attach random matrices to the edges of the graph and get multimatrix models. Additionally, to the stars we attach source matrices. They play the role of free parameters or model coupling constants. The answers for our integrals are expressed through quantities that we call the "spectrum of stars". The answers may also include some combinatorial numbers, such as Hurwitz numbers or characters from group representation theory.We study the information rates of noncoherent, stationary, Gaussian, and multiple-input multiple-output (MIMO) flat-fading channels that are achievable with nearest neighbor decoding and pilot-aided channel estimation. In particular, we investigate the behavior of these achievable rates in the limit as the signal-to-noise ratio (SNR) tends to infinity by analyzing the capacity pre-log, which is defined as the limiting ratio of the capacity to the logarithm of the SNR as the SNR tends to infinity. We demonstrate that a scheme estimating the channel using pilot symbols and detecting the message using nearest neighbor decoding (while assuming that the channel estimation is perfect) essentially achieves the capacity pre-log of noncoherent multiple-input single-output flat-fading channels, and it essentially achieves the best so far known lower bound on the capacity pre-log of noncoherent MIMO flat-fading channels. Extending the analysis to fading multiple-access channels reveals interesting relationships between the number of antennas and Doppler bandwidth in the comparative performance of joint transmission and time division multiple-access.We present a biological fractional n-species delayed cooperation model of Lotka-Volterra type. The considered fractional derivatives are in the Caputo sense. Impulsive control strategies are applied for several stability properties of the states, namely Mittag-Leffler stability, practical stability and stability with respect to sets. The proposed results extend the existing stability results for integer-order n-species delayed Lotka-Volterra cooperation models to the fractional-order case under impulsive control.This manuscript explores fuzzy rule learning for sound synthesizer programming within the performative practice known as live coding. In this practice, sound synthesis algorithms are programmed in real time by means of source code. To facilitate this, one possibility is to automatically create variations out of a few synthesizer presets. However, the need for real-time feedback makes existent synthesizer programmers unfeasible to use. In addition, sometimes presets are created mid-performance and as such no benchmarks exist. Inductive rule learning has shown to be effective for creating real-time variations in such a scenario. However, logical IF-THEN rules do not cover the whole feature space. Here, we present an algorithm that extends IF-THEN rules to hyperrectangles, which are used as the cores of membership functions to create a map of the input space. To generalize the rules, the contradictions are solved by a maximum volume heuristics. The user controls the novelty-consistency balance with respect to the input data using the algorithm parameters.